pub fn new_birthday_probability(n: u32) -> f64 {
    if n >= 365 {
        return 1 as f64;
    }
    let mut result = 1 as f64;
    for i in 0..n {
        result *= (365 - i) as f64 / (365 as f64);
    }
    return (1 as f64) - result;
}
